From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks

TL;DR

This paper introduces an integrability-based method for calculating multipoint conformal blocks in higher-dimensional conformal field theories by relating them to eigenfunctions of Gaudin Hamiltonians.

Contribution

It establishes a novel connection between conformal blocks and integrable Gaudin models, enabling new differential equations for multipoint block evaluation.

Findings

Conformal blocks are eigenfunctions of Gaudin Hamiltonians.

Provides a complete set of differential equations for multipoint blocks.

Lays groundwork for integrability methods in higher-dimensional CFTs.

Abstract

In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal blocks for $N$-point functions may be considered as eigenfunctions of integrable Gaudin Hamiltonians. This provides us with a complete set of differential equations that can be used to evaluate multipoint blocks.